An analog experiment of the parametric instability

Berthet, R.; Petrosyan, A. S.; Roman, Benoît

doi:10.1119/1.1477428

Cited by 22 publications

(20 citation statements)

References 17 publications

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“…The first one is a vertically vibrated layer of fluid on which surface waves are generated by the Faraday instability [21]. 3 The second one is an electronic parametric oscillator, closely described by a Mathieu equation with a cubic nonlinearity [22]. The study of these two systems has been motivated by the fact that many damped modes are present in the one involving surface waves whereas this is not the case for the electronic oscillator.…”

Section: Introductionmentioning

confidence: 99%

Effect of multiplicative noise on parametric instabilities

Berthet¹,

Petrossian

Residori

et al. 2003

Physica D: Nonlinear Phenomena

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We report a study on the effect of external multiplicative noise on parametric instabilities using two different experimental systems: an electronic RLC circuit, parametrically pumped with a voltage-variable capacitor, and surface waves generated by vertically vibrating a layer of fluid (the Faraday instability). Both systems are forced by the superposition of a sinusoidal and a noisy component. We study the statistical properties of the response of both systems to noisy parametric forcing and compare them with theoretical predictions. When the detuning from parametric resonance is such that the bifurcation in the absence of noise is supercritical, both systems behave in the same way under the influence of noise. We find that the effect of noise is twofold: on one hand, it triggers the instability before its deterministic onset under the form of oscillatory bursts; on the other hand, it inhibits the nonlinearly saturated oscillatory response above the deterministic onset. When the detuning is such that the bifurcation is subcritical, we find that the two systems behave differently. In the case of the electronic oscillator, noise mostly triggers random transitions between the two states of the bistable region that exists in the absence of noise, whereas in the surface wave experiment new states are created by noise and the bistable region is strongly enlarged.

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Section: Introductionmentioning

confidence: 99%

Effect of multiplicative noise on parametric instabilities

Berthet¹,

Petrossian

Residori

et al. 2003

Physica D: Nonlinear Phenomena

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“…Consider the parametric RLC oscillator [12], [13] given in figure 2, where L is the inductance, R the resistance, C the capacitance, and the box represents an analog multiplier of gain k and v γ = γcos(ωt).…”

Section: Problem Statementmentioning

confidence: 99%

On the implementation of a parametric oscillator in analog applications

Moreno-Ahedo¹,

Carmona²,

Francisco

et al. 2012

2012 8th International Caribbean Conference on Devices, Circuits and Systems (ICCDCS)

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This paper presents an electronic circuit that exhibits parametric resonance, namely a parametric RLC oscillator. The circuit exploits parametric resonance in an analog application, namely, a gain-frequency dependent switch. In such circuit, when the amplitude and frequency of the parametric excitation varies then a transition curves, in the parameter space, are computed by using an algorithm that calculates the symbolic monodromy matrix. Such curves are interpreted to implement an analog application.

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“…(2) becomes a Mathieu's equation. Parametric resonance of this system in the presence of damping was analysed both theoretically and with an electronic analog circuit [23]. The systems (1) and (2) exhibit normal and anomalous diffusions for certain range of values of the amplitude and frequency of the periodic force.…”

Section: Introductionmentioning

confidence: 99%

Oscillatory variation of anomalous diffusion in pendulum systems

Sakthivel

Rajasekar

2011

Pramana - J Phys

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Numerical studies of anomalous diffusion in undamped but periodically-driven and parametrically-driven pendulum systems are presented. When the frequency of the periodic driving force is varied, the exponent μ, which is the rate of divergence of the mean square displacement with time, is found to vary in an oscillatory manner. We show the presence of such a variation in other statistical measures such as variance of position, kurtosis, and exponents in the power-exponential law of probability distribution of position.

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An analog experiment of the parametric instability

Cited by 22 publications

References 17 publications

Effect of multiplicative noise on parametric instabilities

Effect of multiplicative noise on parametric instabilities

On the implementation of a parametric oscillator in analog applications

Oscillatory variation of anomalous diffusion in pendulum systems

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